Comparing 2 sets of longitudinal data Blood level of a chemical was recorded in children of different ages in 2 studies. Means and variance is available for different ages as shown in following manually created figure: 

I can compare two studies for each age to show if they are different but how can I compare the two full series to say if they are significantly different overall? Which test should I apply? Thanks for your help.
 A: Although it seems like you are comparing two time series, you could instead think of the task as comparing the means of several dependent groups.
This means you could use a multiple comparison procedure that accounts for the dependent nature of the groups.
Wikipedia link to methods
Alternatively, if you don't mind writing a bit of code, you could use bootstrapping to solve the problem:


*

*Take two bootstrap samples of series 1 and one bootstrap sample of series 2.

*Calculate the average absolute difference (AAD) between age groups for the first bootstrap sample of series 1 and the bootstrap sample of series 2. To calculate this metric, for each age subtract the mean of group 1 from the mean of group 2 and take the absolute values of these differences. For easier interpretation, we can record the average of these resulting values and call the result "Series Diff". This operation estimates the natural difference between series 1 and series 2. 

*Calculate the AAD between age groups for the first bootstrap sample of series 1 and the second bootstrap sample of series 1 and call the result "Series Variability". This operation captures the variation of series 1.

*Subtract the "Series Variability" metric from the "Series Diff" metric and save the result and "Final Diff". "Final Diff" can be interpreted to be the final difference between the AAD of series 1 and series 2 after accounting for natural variation in series 1. 

*Repeat the first four bullet points as many times as is reasonable being sure to save the "Final Diff" result each time.

*Pick an alpha level (0.05 is often accepted as reasonable). 

*If the fifth percentile of your data is greater than 0, than with 95% confidence we can reject the hypothesis that series 2 was drawn from the same distribution as series 1. Otherwise, we fail to reject the hypothesis.

